Proceedings of the Institute of Radio Engineers Volume 22, Number 8 August, 1934 ON CONVERSION DETECTORS* BY M. J. 0. STRUTT (Natuurkundig Laboratorium der N. V. Philips' Gloeilampenfabrieken, Eindhoven, Holland) Summary-Conversion detectors for superheterodyne sets are classified in two groups, containing two types each. These types are illustrated in Figs. 1(a), 1(b), 2(a), 2(b), 2(c), 2(d), and 2(e). It has been found possible to represent measured static characteristics (current versus applied voltage) of all types of detectors con- sidered accurately by an equation of the type i = EAnea-V By using this expression for the static characteristics, conversion gain, distortion effects (modulation rise, modulation distortion, cross-modulation), and harmonics (causing whistling notes) could be calculated for all types of conversion detectors. An apparatus is described, permitting of easy measurements of conversion gain and harmonics. Measured and calculated data check as well as could be expected. Con- version gains of more than 400 were found with modern valve conversion detectors. It is pointed out that distortion may be determined by measuring the harmonics. INTRODUCTION ANY possibilities have been proposed hitherto for the use as a N j8 Xfirst detector (modulator) in superheterodyne sets. The ob- ject of this paper is to treat the more common systems the- oretically and experimentally with a view of comparing their relative merits..Before starting this, it might be worth while to give a brief description of these systems. Two main groups of first detectors are considered, indicated by I and II. With the detectors of group I, input signal voltage Ei and local oscillator voltage Eh are put on one single electrode. With group II they are put on different and separate electrodes. As examples of group I we have: I(a) Diode Detectors. The simplest form hereof is contained in Fig. 1(a). The two voltages Eh and Es, issuing from a common tapped coil of small impedance are acting on the diode D in series with an impedance z. Let Wh be the angular frequency (27rXcycles per second) of the voltage Eh and coi of the voltage Ei, then the impedance z is designed to have an appreci- able value only for alternating current of the angular frequency CO= COh -Wi I. For coo we have z = R, at all other frequencies including * Decimal classification: R134. Original manuscript received by the Institute, January 18, 1934. 981 Strutt: Conversion Detectors direct current z = 0. Another form of diode detection is shown in Fig. l(b), where the grid-cathode circuit forms the diode, grid bias being such as to cause grid current flow and the voltage is amplified by the triode. The impedance is now in the anode circuit. 1(b) Variable Slope Detectors. Here also, the circuit of Fig. l(b) illustrates the principle, grid bias being this time such that no grid currents flow. Tetrodes and pentodes may replace the triode of Fig. 1(b). Detection is caused by the variable slope of the (direct current) anode-current grid-tension characteristic. Internal resistance is high. Numerous representatives of group II have appeared recently; some of the more common ones are here dealt with. i~h-E (a) (b) Fig. 1 (a) Diode detector. Two voltages in series (peak values Ei and Eh) coming off a tapped coil transformer C act on the diode D and on the impedance Z, which is in series with the diode. This impedance Z has a zero value for the frequencies of E, and of EA but it has a very large value (e.g., one megohm) for a frequency which is the difference of these frequencies, this difference being the frequency of Eo. (b) Triode detector. Symbols similar to Fig. 1 (a). II(a) Double Grid Detectors. The principle is shown in Fig. 2(a). Grid bias is such that no grid currents flow in the input circuit. More recent forms of this principle are shown in Figs. 2(b), 2(c), 2(d), and 2(e). These embody the essen- tial parts of the valves 2A7 (RCA); E448 (Philips Co., Ltd.), the oc- tode (of Philips), and the "emission valve" of the Hazeltine Corpora- tion, respectively.' The underlying idea of these constructions resides in controlling the slope (anode-current-signal-grid voltage) by a sec- ond grid, upon which the local oscillator voltage Eh is put. By shielding the two grids electrostatically the voltage Eh can be prevented from getting on the antenna and radiating thence. Electron coupling of the grids is, however, not prevented by the shield. Moreover the valves of the groups I(b) and II(a) permit dispensing with an extra oscillator valve, as they can generate the voltage Eh by themselves. II(b) Grid-Anode Detectors. This type is different from 11(a) in as much as the anode is used instead of a second grid (see Fig. 2(e)). By suitably choosing the anode tension, detection in the anode bends is made possible. 982 Strutt: Conversion Detectors It is emphasized here, that detector properties only of the valves, just given as examples, will be contemplated in this article. Generation of local voltage is an essential claim of some of them. These oscillator properties should therefore be considered also, before forming a com- plete view on their relative merits as detector-oscillator valves. How- ever, as will be shown, detector properties alone already involve such complex considerations, that one is justified in putting aside at first the oscillator properties. £ - 5r 2 E 2 r 1Fig. 1 (a).1 anodeandsreen,respetivel .Ote2ybl si i.1() (d) Philleips detctode. (Priscplve. Syhossi-milar to Fig.2( Ithteaddtono. asp atrtessorimsthngrid,ioretoban an inceaedmodulator. reitanceSymbolsasinFg above. (e) Emission valve. (Hazeltine Corporation.) Grids 1 and 2 are screen and oscil- lator anode, respectively. Other symbols as in Fig. 1 (a). (f) Gride-anode conversion detector. Ljocal oscillator voltage is induced in coil C. Other symbols as in Fig. 1 (a). Mathematical Formulation of Valve Charcecteristics. As is well known, some mathematical relation between anode cur- rent and grid voltage must be assumed in order to calculate the per- formance of valves. After several trials, a special formulation of this relation was found, permitting of suficiently close approximation of actual valve characteristics on one side and of relatively easy calcula- 1 H. A. Wheeler, Electronics, p. 76, March, (1933). 983 Strutt: Conversion Detectors 10 5 O'l 2 I 0 -26 -2B -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 Fig. 3-Horizontal axis: grid tension V (Volts); vertical axis: anode current i (milliamperes). Valve RCA 58. Curve calculated from i =3.3 e°080V+8.7 eO.8Yv. Points measured. tion on the other. Dealing, first, with valves of group I, the current i (diode current with type I(a) or anode current with type T(b)) is re- lated to the input voltage V (both direct current) by 10 8 6 5 1/ 3 2 I -28 -26 -21 -22 -20 -18 -16 -1Y -12 -10 -8 -6 -4 -2 0 Fig. 4-Co6rdinates as in Fig. 3. Curve calculated from i-2.60 eO°122v+11.6eO.612v. Points measured. Valve Philips E447. 1/ l1 I __ /1fil - - U.7 I 11 984 n If. Strutt: Conversion Detectors i = Anea v. (1) Here, practically, a finite sum, consisting, e.g., of two or three terms, is meant, n being 1, 2, 3 and so on. Theoretically, it may be shown, that any curve in any interval of V may be approximated by a series (1) as closely as is desired, if the number of terms is taken sufficiently great. In order to show the practical value of the approximation (1), some examples are given in Figs. 3, 4, 5, 6, and 7. Not more than three 41 I 0,1 5 3 2 0,01 A ,nd -10 -9 -8 -7 -6 -5 -4 -J -2 -? 0 Fig. 5-Cobrdinates as in Fig. 3. Curve calculated from i=28.7 el""v. Points measured. Valve Philips E452T. terms are considered in any of these examples, already giving a close approximation to the experimental curve. Coming to valves of the group II, two separate input voltages are to be considered, named Va and Vb respectively. The dependence of the anode (direct) current on these voltages is expressed by = £ C"ea^7v+bnVb (2) Here again, any experimental function of Va and Vb in any interval of these voltages may be approximated as closely as desired by a series, I., I f II I 985 __I_ I 9Strult: Conversion Detectors like (2), if a sufficiently great number of terms is taken. Practically, some two or three will suffice, as is shown by the example, given in Fig. 8. 0o 10 < ~~~~5 3 2 -E --4 3 2 -1 0 Fig. 6-Coordinates as in Fig. 3. Curve calculated from i 11.5 eo28v-1.2 e0 77V +0.18 e 1o(V+) Points measured. Valve Philips E446. 2 I >~~~~~~~~~~~~I 7 7 2 Fig. 7-Co&rdinates as in Fig. 3. In this case anode was diode part of valve Philips E444. Curve calculated from i=0.365 eO0 46V-0.271 e0-61v. Points measured. Thus we have found two functional expressions, (1) and (2), per- mitting to approximate experimental curves very closely. The ad- vantage of these expressions will be shown to be twofold. In the first place, they enable one, to calculate accurately the complete detector performance, if the direct-current characteristic of a detector is known. 986 Strutt: Conversion Detectors 987 Second, they permit of general deductions, independent of any par- ticular detector characteristics. Examples hereof are given below. Calculated Conversion Gain of Type I(a) Detectors. Considering the scheme of Fig. 1(a), a voltage of frequency 10 0,5 0,4 0,3 0'I / 0,001 0,0001 -20 15 /0 5 0 Fig. 8-Co6rdinates as in Fig. 3. This is a double-grid modulator, the anode current depending on the tensions of two grids. The tension of one grid is taken as horizontal axis, while the tension of the other grid is taken as parameter. Curves calculated from: i = 9.8 eO.72Va +03Vb+4.1 eO.54Va+OOVb. Points meas- ured. Experimental valve of this laboratory. W0 = |Wi- hh will be developed across the impedance z = R. Hence, the total voltage, acting on the diode, assuming an additional direct bias tension VO, is Strutt: Conversion Detectors V = Vo + Ei sin coit + Eh sin coAt- Eo coscot. (3) This voltage (3) has to be substituted in (1), in order to get the current i through the detector. This total current i consists of a direct-current part and alternating-current parts of angular frequencies coi, 2coj, 3coi . ; WA, 2COh, 3CWh - * and sums and differences of these quantities. Of this total current i only one component is of interest here; i.e., io cos coot, as this component gives rise to the voltage Eo cos coot = Rio cos coot across the impedance R. The conversion gain of the detector with very small input voltages is defined as Eo i1 =_. (4) Assuming, that the input signal voltage E} is small, such that the rela- tions anEi>l. Then we have 1 - I,(ja,Eh) = Io(janEA) and hence by (5) (5a)g = 1. Strutt: Conversion Detectors Thus, in this case of maximum output voltage Eo, the conversion gain is unity. As it often appears that all terms in the numerator and in the denominator of (5) are positive in actual calculations (see Figs. 3, 4, and 5), the conversion gain decreases, if Eh decreases and also if R decreases. The special value (5a) of (5) may also be deduced in a more aa) T =F} (b) H Fig. 9 (a) Measuring arrangement for determining the conversion conductance and the conversion gain of conversion detectors, as used for type la detectors. The meaning of the number and letter symbols is as follows: 1 =generator of frequency co;; 2 =generator of frequency Wh; la =band-pass filter for the frequency wi; 2a band-pass filter for the frequency Wh; lb =voltmeter for the frequency wi; 2b=voltmeter for the frequency wl, C = autotransformer coil; D = diode under investigation; Z =impedance having a very high value (e.g., one megohm for the frequency j-Wh C= Co) and a small value for all other frequencies including direct current; 3 = milliammeter tuned to the frequency wo and having a very small impedance (e.g., vibration galvanom- eter). A suitable amplifier was used between Z and 3 in Fig. 9(a). (b) Arrangement of Fig. 9(a) set up for the measurement of type 1(b) detectors. Meaning of symbols as in Fig. 9(a). T=valve under investigation. (c) Arrangement of Fig. 9(a) set up for measuring type 2 detectors. H= valve under consideration. Symbols as in Fig. 9(a). elementary way, e.g., using the heterodyne envelope of the two alter- nating voltages2 Es and Eh. In combinations with tetrodes and pen- todes, conversion gains of 500 and more are possible. From (5) and (5a), one can easily see the influence of the bias voltage Vo on the con- " F. M. Colebrook, Wireless Eng., vol. 9, pp. 195-201, (1932). 989 Struit: Conversion Detectors version gain. With given local oscillator voltage Eh, the expressions a,,Eh are greater, if the values of an are greater. If ao,Eh decrease, gs decreases also. Hence, if Vo is adjusted, so as to move to parts of the direct-current detector characteristic, where an is smaller, the conver- sion gain is decreased, other things being equal, and inversely. A different arrangement of conversion detector is obtained, if the impedance z, instead of being only appreciable for the angular fre- quency wo, is made a pure and very large resistance. This case was con- sidered for a straight line and for a square-law static detector charac- teristic3 and for such bias, as to result in half-wave detection. It was shown, that conversion gain amounts to about 0.3. Hence, this ar- rangement is inferior to the one considered above. Measured Conversion Gain of Type l(a) Detectors A measuring arrangement, with which detectors of any type can be investigated, was set up. Its essential parts are contained in Fig. 9(a). In Fig. 9(b) the arrangement is set up for use with type I(b) detectors. Obviously, the same arrangement may be used for measuring the gain of group II detectors, by disconnecting the outputs of the oscillators and connecting them separately to the two detector electrodes, as shown in Fig. 9(c). Several tests were applied to the measuring apparatus, be- fore actually measuring conversion gains. It is noteworthy, that the resistance R of the impedance z (Fig. 9(a)) at the frequency wo was of the order of 101 ohms. Furthermore co1/27r and Wh/27 were both about 20 kilocycles, while wo/2wr was of the order of 1000 cycles. In all tables, given below, Ei and Eh, as is clear from (3) are amplitude values, i.e., N/2 times the effective voltages. We secured the following data for a special detector (diode part of valve Philips E444) Ei (volts) 0.1 0.1 El, (volts) 3 4 gi (meas.) 0.94 0.98 9p (calc.) 0.93 0.97 The coincidence between observed and calculated values (by the aid of (5)) is as good as could be expected. Calculated and Measured Conversion Gain of Type l(b) Detectors. With type I(b) detectors, it will be assumed throughout, that in- ternal resistance of the valves (being tetrodes or pentodes) is large and hence conversion gain principally dependent on exterior (anode) im- pedance. It is more convenient, therefore, to consider primarily the conversion conductance Sc instead of the conversion gain g9. This con- 3 W. R. Bennett, Bell Laboratories reprint No. 724. 990 Strutt: Conversion Detectors version conductance Sc is defined as follows: The anode current i has one component io cos wot. And one can write, io = ScEi. (6) Taking, V = Vo + Ei sin wit + Eh sin coht (7) in (1), the conversion conductance Sc can easily be calculated and is found to be (see appendix B) 2 1 1 =S= E E AneanVo - Il(ja Eh) . I,(janEi) . (8) This equation holds good for any values of Ei and Eh. It simplifies, if Ei is small, such that anE Strutt: Conversion Detectors the common mutual conductance S of the same valve, if used as a high-frequency amplifier. The value of S, by inserting V = Vo+E0 sin wit in (1), is found to be 9i S = (9) By (1), (9) yields S = EAn eanvoan (9a) Comparing this with (8b) and bearing in mind, that with the latter equation anEh Strutt: Conversion Detectors z =R = 0. 5 * 106 ohms at the angular frequency co0, conversion gain will be something like 400. It is emphasized, that this gain is not merely a theoretical value, but was actually measured in experiments, con- ducted by the author in this laboratory. -30 Fig. 10 0 (c) Full curve numbered 1: Vertical axis as in Fig. 10(a). Horizontal axis bias volts of grid for volume control, while local oscillator voltage was 13 volts peak value. Dotted curve calculated from (8a); full curve measured. Curve numbered 2 gives measured values of second harmonic; vertical axis for this curve is microamperes/volts squared. Curve numbered 3 gives measured values of third harmonic. Vertical axis for this curve is microamperes/cube of input volts. Valve E447. Conversion Cain of Group II Detectors. We shall start with a discussion of type II(b) detectors. An es- sential condition with these detectors is, that the anode current de- 993 Strutt: Conversion Detectors pends markedly on the anode voltage, as is seen by (2). Hence, valves used as type 11(b) detectors cannot have a very great interior resist- ance. This low interior resistance results in a poor conversion gain, though conversion conductance may be not so bad. This general con- clusion has been borne out by experiments.5 Obtained conversion gains with a screen-grid valve and, e.g., 105 ohms in the anode were about 0. 6. If compared with the gains, obtained with type I(a) and type I(b) detectors, this value appears so small, that no further time should be spent on type II(b) detectors. Coming now to type 11(a) detectors, interior resistance will be as- sumed large, as compared with exterior impedance in the anode circuit 300 _ 100 10 20 X 40 Fig. 11-Coordinates as in Fig. 10(a). Experimental type of Philips octode valve. Curve calculated by (11). Points are measured values. Publication data of these octodes now show S, = 600. at the angular frequency wo. Hence, conversion conductance is first considered, instead of conversion gain. Inserting Va = Va0+ Ei sin wit; (10) Vb = Vbo + EA sin Coht, in (2), one obtains (see appendix C) 211 Sc = -E C'eanVao+bnvbo -l(janEi) , Il(jb.Eh) (11) Ei~~~~ Here, S, is quite similarly defined as with type l(b) detectors (see (6)). Considering the case, that Ei and Eh are both small (anEi Strutt: Conversion Detectors 2 (libSC = 2- E C,,eanvao+bnvbo+bnEh (llb) Hence, if Vbo+Eh is constant, Sc decreases with increasing Eh in this region. Just as was already shown with type I(b) detectors, conversion conductance has a maximum value as a function of Eh, by (11(a)) and (11(b)). Calculated and observed values of Sc are compared in Fig. 11. Conversion gains of more than 200 are obtained with commercial type II(a) detectors These gains do not compare too unfavorably with those of type I(b) detectors. They are, however, often lower than the gains of type I(b) detectors. Modulation Rise, Distortion, and Cross-Modulation. Though a very important item in the comparison of conversion de- tectors, gain is not the only important factor. The several distortion effects, connected with not straight tube characteristics, should be taken into consideration. They are the same ones, as occur with high- frequency amplifiers.6 If Ei is no longer very small, we have Eo = g1Ei + q3Ej3 + * * * (12) (even powers of Ei do not occur; see appendix D). The following values are obtained for the distortion effects M,'-M 93 3 = -e2(2 M2) (13) M 91 4 Here Ei=e(l+M cos pt). Furthermore M1' is the modulation depth of Eo with the angular frequency p. Hence (13) expresses the modulation rise. Besides a modulation of angular frequency p, the output voltage Eo has also a modulation M2' with the angular frequency 2p (see ap- pendix D). _=--~~e2M. (14) M gi 2 This is obviously a measure for the distortion of modulation. Taking an input signal e sin wit+Ek(l+Mk cos pt) sin Wkt, where the latter term is a crossing signal, the modulation depth Mo of the output signal voltage Eo with the modulation of the crossing signal is (see appendix D) Mo = 4E2kMk-. (15) 6 R. 0. Carter, Wireless Engineer, vol. 9, pp. 429-438? (1932). 99.5 Strutt: Conversion Detectors This is cross modulation. Expressions (13), (14), and (15) only hold good for small input voltages Ei, such that anEi Strutt: Conversion Detectors of the incoming signal is assumed to be wi, the fundamental angular frequency of the local oscillator COh. The band-pass filter behind the first detector only passes the angular frequency coo= ci-WhJ. But the modulator, if not perfect, will also produce angular frequencies 2wo, 3w0, etc., even if the local oscillator and incoming signal are ideal, i.e., purely sinusoidal. Hence, if an incoming signal Wi' occurs (see Fig. 12), such that wi'-_Wh = 'coo, the second harmonic, generated by the de- tector, will be 2X 'coo =coo, i.e., will be passed by the filter. This is then heard as a whistling note, while adjusting the local oscillator so as to receive the signal wo. Similarly, a signal coi", such as | 3-W= will produce a whistle by the third harmonic, generated by the detector, i.e., 3 X coo =coo, and so on. These whistles are present even with perfect local oscillators and incoming signals; they will be designated as de- tector whistles. A second group of whistling notes is found, if the de- tector is considered as perfect, i.e., generating not one single harmonic of wo, if coi and WA were purely sinusoidal. Consider a local oscillator, producing the angular frequencies 2Wh, 3Wh, 4CWh, etc., besides the wanted Wh. Then, if 2WA-Wi/ =coo) a whistle is heard, and similarly for the higher harmonics. These whistles may be diminished by choosing a low wo frequency, such that the signal of angular frequency coi' is al- ready much attenuated by the selective circuit before the first detector. If the incoming signals are not purely sinusoidal, their harmonics will result in whistles, while adjusting the local oscillator so as to receive a different signal. This effect is generally small. All the whistles, just considered, are called input whistles, as they are caused by the input not being purely sinusoidal. A third group of whistling notes is caused by the detector producing harmonics of the input frequencies. Thus, with a local oscillator CWAh, if a frequency 2Wh is formed in the output cir- cuit, this can combine with a not wanted signal coi', such that |-2WoA = Wo and causes a whistle. For the prevention of the mixed whistles, just considered, a choice of low coo may be favorable, for then no appreciable signal wi' will be passed by the selective circuit before the first detector. If the impedance z, being equal to R at the frequency CO, is sufficiently selective and the other impedances in the input cir- cuit sufficiently small, no considerable voltage of frequency 2wa can be formed in the input circuit. Of course, a serious whistle may be pro- duced by the so-called mirror effect, the local oscillator causing a passed wo frequency on both sides of the oscillator ¢Jh- For the prevention of this mirror effect a high coo is favorable. In what follows, detector whistles will be considered quantitatively. Considering, first, type I(a) detectors, the voltage E2 cos 2Wot, where coo= Wh-Wil and z=R for 2wo is found to be (see appendix F) 997 Strutt: Conversion Detectors 1 1 2 Anan I2(ja,Eh) ) eanvo. (19) 21 -+ E A,Lanlo(jaflEh)R Similarly, 1 1 EZAnan3 , I3janEh) Es= 3 1 . 3 eanVo (20)2213 1 - + E AnanI0(janEh) From these equations, some important conclusions on the whistling tones may be drawn. It is seen that the second whistle (19) is propor- tional to the second power of whistling signal input voltage, the third whistle (20) proportional to the third power, etc. Furthermore, if the local oscillator voltage Eh is small, the second whistle (19) is propor- tional to Eh2, the third whistle (20) to Eh3, etc. It is interesting to know the ratio of the whistling voltages E2, E3, etc., to the conversion voltage Eo. Of course, one should remember, that Ei means the wanted input signal voltage in (5) for the conversion voltage and means the un- wanted (whistling) input signal voltage in (19) and (20). If we regard E2/Eo, E3/Eo, etc., as a function of Eh only, it is seen from the afore- said equations that these ratios start with zero and increase to be finally constant, if Eh increases from zero upwards. Finally, from (13), (14), (15), (16), and (20) it may be deduced that if aEh»>>l the dis- tortion effects may be determined by measuring the third whistle (20). In fact, they are proportional to (20) (see appendix G). Coming to type 1(b) detectors the voltages E2, E3, etc., are given by the equations (see appendix F) 1 E2 = i2R =--RE 2 x AfeanVoI2(jalEh)af2; (21) 1 1 E3 = i3R = - REi3 > A,eanVo - I3(janEh)an3, etc. (22) 24 ,I From (21) and (22) similar conclusions may be drawn, as stated above for type 1(a) detectors. Moreover, it is seen from (17), (18), (21), and (22), that for small values of Eh: anEh1), S3/S1 is proportional to E3/Eo (see appendix G). This remark includes an easy way of meas- uring distortion effects with type I(b) detectors by simply measuring their harmonics. 998 Strutt: Conversion Detectors Finally, with type II(a) detectors, we have 12E2= i2R = - RE,2 E CeanVao+bnVboI2(jbnEh)a.s; (23) 4 1 1 Es = isR = - REi3 I CneanVao+bnVbo I3(jbnEh)an8, etc. (24) 24 With regard to the proportionality of S3/S1 (i.e., of the distortion effects) to the ratios E2/Eo and E3/Eo, quite the same remarks hold, as were brought forward above in connection with type I(b) detectors. Measurements of Harmonics. The measuring apparatus of Figs. 9(a), 9(b), and 9(c) was utilized for the present purpose. The oscillator frequency wi was so adjusted, that Wi-Wh I ==wo/2 for measuring the second harmonic. It was so adjusted, that 'i. -COh =co0/3 for the third harmonic, etc. Measurements were further carried out in quite the same way, as was described formerly for the conversion gain gi. The following table shows the comparison of measurements and calculations for the second harmonic etc., of a type 1(b) detector, in this case a Philips E447 valve. TABLE I Grid bias volts -14 -16 -17 -20 -22 -23 Second harm. calc. 51 40 1.4 1.2 Second harm. obs. 46 44 1.5 1.0 Third harm. calo. 15 5 2. 8 0.12 0.078 Third harm. obs. 16 5 2. 8 0.13 0. 075 Second harmonic expressed in microamperes/input volts squared. Third harmonic: microamperes/ cube of input volts. In general, the ratios E2/Eo, E3/Eo, etc., were found to be some per cents at most, for commercial detector valves. It is noticeable, that type I(a) detectors are in general not inferior to type I(b) and type II(a) detectors, as regards harmonics and distortion effects. ACKNOWLEDGMENT The author takes pleasure in expressing his appreciation of the assistance given by Mr. N. S. Markus and by Mr. C. P. Fritzius in the experiments and measurements described in this paper. APPENDIX A In order to derive the expression for the conversion gain of a diode, use is made of the series expansion7 7 G. N. Watson, "Bessel Functions, " p. 369, eq. (3). 999 Strutt: Conversion Detectors co ea sinwt = Io(ja) + 2 E I2,m(ja) cos 2mrt rn=l 2 00 + . E I2m+1(ja) sin (2m + 1)cAt. .7 m=O Here Im(ja) is Bessel's function of the first kind, of order m and with the argument ja, wherej= + V/-1. Two properties of Bessel's functions are used in the course of these calculations: lim| Im,X), = m-= m(m-1) 2.1; Xo-+ 2 |m ex lim I,,,(jx) =, x _+ o _0_7rx giving respectively the values of Bessel's functions for small and for large arguments. Tables of the functions lo, I1 are available.7 The voltage V, to be inserted into the equation of the static diode character- istic isZ AneanV V = Vo + Eh sin Cht + Ei sin coit - Eo cos coot. Assuming Ei and Eo to be so small, that anEiK Strutt: Conversion Detectors Now the left side of (1) also contains a component io cos oot, propor- tional to cos cwot. Equating these components on both sides of (1), using (2), yields =o R = E AnFonR or, Eo EAn,eanvoan, Ii(janEh) E =l 1= - E + Z AnIo(ja.Eh)aneanvoR which is (5) of the text. APPENDIX B With type I(b) detectors we have i = Z AneanV and, V = VO + Ei sin wit + Eh sin COt. Using the same series expansions as in the preceding appendix A, one obtains for the current io cos coot) where wo= jWh-Wi , the expression io 2 1 1 E = SC = EE AneaVo -Il(ja.Eh) -I,(janEi). Moreover, the current components i2 cos 2Wot, i3 cos 3Wot, i4 cos 4Wot, etc., are easily found to be i2 = 2E Ar,ean;o12(janEh)2(janEi); 1 1 i3 = 2 E AneanVo -I3(janEh) I3(janEi), etc. APPENDIX C Type II(a) detectors have an anode current i, depending on the grid tensions Va and Vb by i = E CeanVa+bnVb. Inserting Va = Vao + Ei sin cit and Vb = VbO+ EA Sin cWht 1001 Strutt: Conversion Detectors and using the series expansion, given in Appendix A, one finds for the current component io cos cot, where coo = h - iI the expression, io 2 1' 1 = -E CneanVao+bnvbo -I1(ja.Ej) , II(jb.)Eh).EJi EI a It is a simple matter to pick out the harmonic current components i2 cos 2wot, i3 cos 3co0t, etc. One obtains i2 = 2 E C,eanVao+bnvboI2(ja,Ei)I2(jbnEh); 1 1 is = 2 CEGeanVaO+bnVbO I3(janEi) I3(jbnEh), etc. 3 a APPENDIX D Considering first type I(a) detectors, one can show, that the volt- age Eo contains only odd powers of Ei. The even powers of Ei in the expansion eEisinwit = 1 + Ei sin it + -2sin2 coat + -j3 sin3 wit + * * cannot give rise to terms, containing the angular frequency Co= IWh-WiI. Similar remarks hold for type 1(b) and for type II(a) detectors. This may be seen, for the former type, from the expression: 1 1 Eo = R* 2E AneanVo - II(janEi) - Ii(ja"Eh), 3 3 where 1/j 1l(janEi), by the well-known series expansion,7 contains only odd powers of Ei. Quite the same reasoning holds for type II(a) de- tectors. Taking, Eo = gqEj + g3Ej3 + and, Ei = e(l + M cos pt), one obtains 3 Eo = gle(l + M cos pt) + g3e3( 1 + 3M cos pt + M2 cos 2pt 3 1 3\ +-M2 +i M3 cos 3pt +--- M3cos.pt) + Loc. cit., p. 15. 1002 Strutt: Conversion Detectors or, Eo = gle + g3e( 2 /M2 + gjeM + 3g3e3M + - g3e3M3) cos pt + (U3e3 2 cos 2pt+ ge3M3 cos 3pt + Hence the modulation depth M1' of Eo with the angular frequency p is given by (13) of the text. Similarly, from the above expansion, the expressions for M2', being the modulation depth of Eo with the angular frequency 2p, and M3', being the modulation depth of Eo with the angular frequency 3p, are easily found (see (14) of the text). In order to calculate the cross-modulation coefficient Mo, take E = e+Ek(1+Mk cos pt) in the development Eo=g1, E +g3E 3+ The modulation depth of Eo will be found as in (15) of the text. APPENDLX E The calculation of 93 for type I(a) detectors may be performed as follows: The voltage V = - Eo cos coot + Ei sin cit + Eh sin COht is put into the equation of the static characteristic, while Vo= 0 i = Anean7 . Picking out the component io cos coot, by using the series development formulas of Appendix A, and remembering, that io = Eo/R one obtains E0t 1 1 L 1 1 Eo= I (gjEj + g3Ej8)- E A.(ang,Ei + a.g3Ei' + -- a,3lg,Es3R R 8 + -gla3Ej3)Io(janEh) + E A.(a.Ei + -a.3g2E,3 4 4 +- an3Ei3) -I,(jancEh) + E A.(- an3glE;3)I2(ja.Eh). From this equation one finds for g9 the value of Appendix A and (5). For g3 one obtains (16) of the text. The expression (17) for S3 is found by inserting V = Vo+Ej sin cowt +EA sin coht into the equations of the static characteristic: i= eanv.7 1003 Strutt: Conversion Detectors Picking out the terms of frequency coo, one obtains 10~ ~ 1 E- = E A,AeanVo . Il(janEh)a, + Ei2 s Aea,Vo I,Il(janEh)an3 Ei ~~~~~~~~~8 - S1 + S3Ej2. whereby (17) of the text results. Similarly (18) is obtained. APPENDIX F Equation (19) results, if V= -E2 cos 2coot+Ei sin oit+Eh sin (Jht is put into the static characteristic equation, where i2=E2/R. In order to obtain (20), V should be taken to equal -E3 cos 3coot+Ei sin woit +Eh sin cOht. Equations (21) and (22) may immediately be written down from the last two equations of Appendix B, remembering, that for small values of Ej(anEj1) we have -by (20) and (5) (assuming Vo = 0, though this condition is not essential), E1 A.a. 3eanEh _ Eo 24 Ann 1E3 1 E AnAnaeamEh V- -~E V27r-anEh Under the same condition for Eh one obtains (8 91 + -12 - A913)Anan3eanEh 1 93 8 8 4 8 V\2wranEh g1 AnaneanEh Ae27ranEh Hence, E = 2 E 2 ( 8 - g, + g12 -8 g33)-1 . 1004 Strutt: Conversion Detectors With type I(b) detectors, the case of small Eh(alEhK Strutt: Conversion Detectors (3) E. V. Appleton, "Thermionic Vacuum Tubes," Methuen and Co., (1932). (4) E. V. Appleton and D. Boohariwalla, "The mutual interference of wireless signals in simultaneous detection, " Wireless Eng., vol. 9, pp. 136-139, (1932). (5) H. Ataka, "On the modulation of an ultra-short wave by a modulated me- dium wave and its detection," Jour. I. E.E. (Japan), vol. 53, no. 540, pp. 54-55, (1933). (6) S. Ballantine, "Detection at high signal voltages," PROC. I.R.E., vol. 17, pp. 1153-1177; July, (1929). (7) A. C. Bartlett, "The calculation of modulation products," Phil. Mag., vol. 16, pp. 845-847, (1933). (8) W. R. Bennett, "New results in the calculation of modulation products," Bell Sys. Tech. Jour. vol. 12, pp. 228-243, (1933). (9) E. A. Biedermann, "Some notes on the use of a diode as a cumulative grid rectifier," Wireless Eng., vol. 10, pp. 123-133, (1933). (10) H. A. Brown and C. T. Knipp, "Power detection characteristics of pentode tubes," Electronics, pp. 126-127; April, (1932). (11) H. A. Brown, G. W. Pickels, and C. T. Knipp, "Detector distortion at low input signals," Radio Eng., vol. 12, pp. 21-23, (1932). (12) C. S. Bull, "Non-linear valve characteristics. A brief discussion of their use," Wireless Eng., vol. 10, pp. 83-88, (1933). (13) M. V. Callendar. "A note on demodulation under practical conditions," Wireless Eng., vol. 10, pp. 480-483, (1933). (14) E. L. Chaffee, "Theory of Thermionic Vacuum Tubes," McGraw Hill Co., (1933). (15) W. T. Cocking, "Comparing detector valves," Wireless World, vol. 28, pp. 427-429, (1931). (16) R. de Cola, "An analysis of power detection," PROC. I.R.E., vol. 21, pp. 984-989; July, (1933). (17) F. M. Colebrook, "The theory of the straight line rectifier," Wireless Eng., vol. 7, pp. 595-603, (1930). (18) F. M. Colebrook, "The frequency analysis of the heterodyne envelope," Wireless Eng., vol. 9, pp. 195-201, (1932). (19) E. J. C. Dixon, "The heptode a novel thermionic valve," P. 0. Elec. Eng. Jour., vol. 24, pp. 299-302, (1932). (20) C. Fayard, "Elementary theory of a system of multiple modulation of an r. f. oscillation," l'Onde A'lectrique, vol. 12, pp. 295-325, (1933). (21) C. B. Fisher, "S. g. valve as superhet detector," Wireless Eng., vol. 10, pp. 541-542, (1933). (22) W. F. Floyd, "A note on interference tones in superheterodyne receivers," Proc. Phys. Soc., vol. 45, pp. 610-616, (1933). (23) Y. Fukuta and E. Kido, "Graphical determination of the detection char- acteristics of a triode," Rep. Radio Res. (Japan), vol. 13, pp. 8-9, (1933). (24) W. Ch. van Geel, "On rectifiers," Zeit. fiir Physik, vol. 69, p. 765, (1931). (25) W. Ch. van Geel, "Stopping layer of rectifiers," Nature, vol. 132, p. 711, (1933). (26) W. Ch. van Geel and H. Emmens, "On rectifiers," Zeit. fur Physik, vol. 87, p. 220, (1933). (27) W. Greenwood and S. J. Preston, "Quality detectors. A survey of rectifica- tion," Wireless Eng., vol. 8, pp. 648-658, (1931). (28) Y. B. F. J. Groeneveld, B. van der Pol, and K. Posthumus, "Grid detec- tion," Zeit. furHochfrequenz., vol. 29, p. 139, (1927). (29) C. D. Hall, "The estimation of the sensitivity of the grid rectifier for large inputs," Wireless Eng., vol. 7, pp. 668-670, (1930). (30) S. Harris, "Cross modulation in r-f amplifiers," PRoc. I.R.E., vol. 18, pp. 350-354; February, (1930) (31) J. F. Herd, 'Some measurements on optimum heterodyne," Wireless Eng., vol. 7, pp. 493-499, (1930). (32) H. E. Hollmann, "Push-pull brake field audion as a receiver for decimeter waves," Zeit.fiirHochfrequenz., vol. 42, pp. 185-190, (1933). (33) H. E. Hollmann, "Brake field audion controlled without power expendi- ture," Elek. Nach. Tech., vol. 11, pp. 3-15, (1934). (34) W. Jackson, "Modulation and the heterodyne," Wireless Eng., vol. 8, pp. 425-426, (1931). 1006 Strutt: Conversion Detectors (35) L. B. W. Jolley, "Alternating-Current Rectification and Allied Problems," Chapman and Hall, London, (1926). (36) J. Kammerloher, "The h.f. s.g. valve as an anode bend detector," Elek. Nach. Tech., vol. 10, pp. 345-352, (1933). (37) W. Kautter, "Double anode valves for anode bend detection and retro- action," Telefunken Zeitung, vol. 14, no. 65, pp. 46-51; November, (1933). (38) C. E. Kilgour and J. M. Glessner, "Diode detection analysis," Proc. I. R. E., vol. 21, pp. 930-943; July, (1933). (39) K. Kotschubey, "Mercury arc power rectifiers for wireless stations," Wire- less Eng., vol. 11, pp. 130-133, (1934). (40) M. Lambrey and S. Krauthamer, "Two grid valves as frequency changers," Comptes Rendus, vol. 198, pp. 156-158, (1934). (41) W. B. Lewis, "The detector," Wireless Eng., vol. 9, pp. 487-499, (1932). (42) H. W. Lord, "A life test power supply using Thyratron rectifiers," PROC. I. R. E., vol. 21, pp. 1097-1102; August, (1933). (43) G. S. C. Lucas, "Distortion in valve characteristics," Wireless Eng., vol. 8, pp. 595-598; pp. 660-661, (1931). (44) G. S. C. Lucas, 'The graphical solution of detector problems," Wireless Eng., vol. 9, pp. 202-207; pp. 253-258, (1932). (45) C. L. Lyons, "The pentagrid converter," Wireless World, vol. 32, pp. 347- 348, (1933). (46) E. D. McArthur, "Electronics and electron tubes," Gen. Elec. Rev., vol. 36, pp. 136-138; pp. 177-181, (1933). (47) D. McDonald, "The design of power rectifier circuits," Wireless Eng., vol. 8, pp. 522-531, (1931). (48) E. Mallett, "Apparent demodulation," Wireless Eng., vol. 9, pp. 248-252, (1932). (49) E. B. Moullin, "The detection by a straight-line rectifier of modulated and heterodyne signals," Wireless Eng., vol. 9, pp. 378-383, (1932). (50) J. A. Moyer and J. F. Wostrel, "Radio Receiving Tubes," McGraw Hill Co., (1931). (51) W. Mulder, Dissertation, Delft, (1934). (52) J. R. Nelson, "Notes on grid circuit detection," PROC. I.R.E., vol. 17, pp. 551-561; March, (1929). (53) J. R. Nelson, "Grid circuit power rectification," PROC. I.R.E., vol. 19, pp. 489-500; March, (1931). (54) J. R. Nelson, 'Grid circuit linear detection," Radio Eng., vol. 11, pp. 32-34, (1931). (55) J. R. Nelson, "Some notes on grid circuit and diode rectification,", PROC. I.R.E., vol. 20, pp. 989-1003; June, (1932); pp. 1971-1974; December, (1932). (56) J. R. Nelson, "Considerations on detector output tube systems," Elec- tronics, vol. 6, pp. 94-95 and 98, (1933). (57) E. Peterson and C. R. Keith, 'Grid current modulation," Bell Sys. Tech. Jour, vol. 7, pp. 106-139, (1928). (58) H. Pitsch, "Retroaction coupling with binodes," Funktech. Monatshefte, no. 12, p. 487-488, (1933). (59) R. C. .! "Use of 1A6 tube," Radio Eng. vol. 13, no. 10, p. 26; October, (1933). (60) E. Y. Robinson, "Pentode as detector amplifier," Wireless World, vol. 27, pp. 238-240, (1930). (61) G. D. Robinson, "Test procedure for detectors with resistance coupled output," PROC. I. R. E., vol. 19, pp. 806-811; May, (1931). (62) Y. Rocard, "Two grid valves as frequency changers," Comptes Rendus, vol. 198, pp. 554-556, (1934). (63) H. Roder, "Some notes on demodulation," PROC. I.R.E., vol. 20, pp. 1946-1961; December, (1932). (64) H. Roder, "Superposition of two modulated radio frequencies," PROC. I.R.E., vol. 20, pp. 1962-1970; December, (1932). (65) H. 0. Roosenstein, "Demodulation which is little affected by fading," Zeit. fur Hochfrequenz., vol. 42, pp. 85-89, (1933). (66) H. Rudolph, "Maximum aperiodic amplification and anode bend detec- tion," Archiv Elektrotech., vol. 24, pp. 1-3, (1930). 1007 Strutt: Conversion Detectors (67) R. Ruedy, "Rectifier characteristics and detection diagrams," Phys. Rev., vol. 35, p. 129, (1930). (68) I. Runge and H. Beckenbach, "Ein Beitrag zur Berechnung des Parallel- wechselrichters, " Zeit. Tech. Physik, vol. 14, pp. 377-384, (1933). (69) E. Severini, "Equivalent entrance resistance of grid leak triode detector," Alta Frequenza, vol. 2, pp. 537-547; October, (1933). (70) C. N. Smyth and J. Stewart, "The double diode triode," Wireless World, vol. 32, pp. 355-356, (1933). (71) A. L. M. Sowerby, "The penthode as an anode rectifier," Wireless World, vol. 25, pp. 391-394, (1929). (72) K. Steimel, "Mixing and fading hexodes, " Telefunken Zeit., vol. 14, no. 65, pp. 33-46, November, (1933). (73) M. J. 0. Strutt, "Rectification analysis, " Zeit. far Hochfrequenz., vol. 42, pp. 206-208, (1933). (74) M. J. 0. Strutt, "Radio receiving tubes of large interior resistance. B. modulator (detector) tubes," Zeit. ffir Hochfrequenz., vol. 43, pp. 18-22, (1934). (75) T. Tanasescu, 'The performance of a thermionic tube as a rectifier." Wireless Eng., vol. 1 1, p. 68-71, (1934). (76) Telefunken Co., "Hexodes, a new type of receiving valve," Elek. Zeit., vol. 54, p. 611, (1933). (77) F. E. Terman and B. Dystart, "Detection characteristics of screen-grid and space-charge grid tubes," PROC. I.R.E., vol. 17, pp. 830-833; May, (1929). (78) F. E. Terman and Thomas M. Coogin, "Detection characteristics of three- element vacuum tubes," PROC. I.R.E., vol. 17, pp. 149-160; January, (1929). - (79) F. E. Terman, "Notes on the Wunderlich tube (for grid leak power de- tection)," Electronics, p. 148, April, (1932). (80) P. K. Turner, "A new valve characteristic," Wireless Eng., vol. 9, pp. 384- 387, (1932). (81) A. G. Tynan, "Modulation products in a power law modulator," PROC. I.R.E., vol. 21, pp. 1203-1209; August, (1933). (82) R. Urtel, "The mode of action of diode detection," Telef. Zeit. vol. 14, no. 64, pp. 30-45, (1933). (83) G. Varret, "Detection of modulated waves," l'Onde Alectrique, vol. 11, pp. 315-328, (1932). (84) N. Vermes, "General analysis of amplification and detection by ther- mionic valves," Annalen der Physik, vol. 4, pp. 943-969, (1930). (85) J. C. Warner, E. W. Ritter, and D. F. Schmit, "Recent trends in receiving tube design." PROC. I.R.E., vol. 20, pp. 1247-1262; August, (1932). (86) Westinghouse Brake and Shaxby Signal Co., "The Westector," Wireless World, vol. 32, pp. 173-174, (1933). (87) H. A. Wheeler, "The hexode vacuum tube," Radio Eng., vol. 13, no. 4, pp. 12-14, (1933). (88) E. L. C. White, "The s.g. valve as a frequency changer in the superhet," Wireless Eng., vol. 9, pp. 618-621, (1932). (89) J. P. Woods, "The calculation of detection performance for large signals," Physics, vol. 2, pp. 225-241, (1932). 1008